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Discussion Papers
Why are More Redistributive Social Security
Systems Smaller? A Median Voter Approach
Marko Koethenbuerger
Center for Economic Studies, University of Munich, and CESifo
Panu Poutvaara
University of Helsinki and HECER
Paola Profeta
Università Bocconi
Discussion Paper No. 83
November 2005
ISSN 1795-0562
HECER – Helsinki Center of Economic Research, P.O. Box 17 (Arkadiankatu 7), FI-00014
University of Helsinki, FINLAND, Tel +358-9-191-28780, Fax +358-9-191-28781,
E-mail [email protected], Internet www.hecer.fi
HECER
Discussion Paper No. 83
Why are More Redistributive Social Security
Systems Smaller? A Median Voter Approach *
Abstract
We suggest a political economy explanation for the stylized fact that intragenerationally
more redistributive social security systems are smaller. We relate the stylized fact to an
"efficiency-redistribution" trade-off to be resolved by political process. The inefficiency of
social security financing is due to endogenous labor supply. Using data on eight European
countries, we find that the stylized fact and a considerable degree of cross-country
variation in contribution rates can be explained by the median voter model.
JEL Classification: D72, D85, L14
Keywords: Earnings-related and flat-rate benefits, applied political economy, public
pensions, labor supply.
Marko Koethenbuerger
CES
University of Munich
Schackstrasse 4
D-80539 Munich
GERMANY
e-mail: [email protected]
Panu Poutvaara
Paola Profeta
Department of Economics
University of Helsinki
P.O. Box 17
FI-00014 University of Helsinki
FINLAND
Università Bocconi
IEP
Via Gobbi 5
20136 Milano
ITALY
e-mail: [email protected]
e-mail: [email protected]
* Comments received at presentations at CES (Munich), CEBR (Copenhagen), Mannheim, Tilburg, at the
IIPF meeting in Milan 2004, at the RES meeting in Nottingham 2005, at the CESifo area conference in
Munich 2005, at the Norwegian-German Seminar on Public Economics in Garmisch-Partenkirchen 2005 and
at the CEPR/RTN Final conference on "Financing Retirement in Europe" in London 2005 are gratefully
acknowledged. In particular, we wish to thank Edmund Cannon, Guenther Fink, Vincenzo Galasso, Michael
Hoel and Jean-Marie Lozachmeur for valuable comments. We acknowledge financial support from the
Danish Social Science Research Council, without implicating the sponsor for the views expressed.
1
Introduction
Old-age pensions are at the core of public sector in almost all OECD countries. In 2001, the 15
EU member states spent on average 8.8 percent of their GDP on public old-age pensions (OECD,
2004). But while united in fiscal importance, pension systems are divided in how benefits
are linked to past earnings. In earnings-related (“Bismarckian”) public pension programs,
pensions are perceived as a form of postponed wage income, intended to replace earnings during
retirement. Such benefit rules dominate in Continental Europe, including France, Germany
and Italy. In the competing tradition of rather flat-rate (“Beveridgean”) pensions, the stated
aim of old-age benefits is to guarantee a reasonable standard of living for the elderly, and
benefits are correspondingly flat-rate or close to it. Countries with close to flat-rate pensions
include Japan, the United Kingdom, and the United States.1 Since contributions are typically
proportional to earnings, flat-rate benefit formulas imply more intragenerational redistribution
than in earnings-related systems.
Countries with earnings-related public pension programs have considerably higher contribution rates than those with flat-rate benefits. Disney (2004) reports that the effective contribution rates in the 10 OECD countries dominated by flat-rate systems varied between 14,7
percent in Australia and 23,7 percent in the United Kingdom in 1995. The range in the 12
OECD countries with more earnings-related benefits was between 22,4 percent in Germany and
57,7 percent in Greece. The average effective contribution rate was 19 percent in countries with
flat-rate benefits, and 35 percent in countries with earnings-related benefits.2
In this paper, we analyze to what extent the stylized fact can be reconciled by a “efficiencyredistribution” trade-off about which the political process compromises. In particular, we
ask whether a median voter model is able to explain the positive correlation between the
size of the social security system and the degree to which pension benefits depend on past
contributions. We first present a theoretical model where citizens vote on the social security
contribution rate in the presence of endogenous labor supply. Citizens differ in two dimensions,
age and productivity. There are three cohorts, the young, the middle-aged and the old, and five
productivity classes within each cohort. Social security benefits encompass an earnings-related
and flat-rate component. As contributions towards earnings-related benefits cause smaller
labor supply distortions, the efficiency cost of social security financing is lower the smaller
the redistributive flat-rate pillar. Thus, the correlation between the size of social security and
the degree to which pensions are earnings-related depends on the age and productivity of the
politically-decisive voter.
In a second step, we perform a numerical analysis that delivers the political equilibrium
social security contribution rates for Austria, France, Germany, Greece, Italy, Portugal, Spain
and the United Kingdom. The numerically solved median voter model predicts that countries
with more earnings-related public pension programs vote for a higher contribution rate than
those with more flat-rate benefits - a prediction which is in line with the stylized fact.
Although being a cornerstone in economic policy reasoning, the trade-off between efficiency
1
In most countries, social security has both a flat-rate and an earnings-related component, the relative
importance of which differs. We choose labels for countries according to which component is more pronounced,
taking our classification from Disney (2004) who labels earnings-related systems Bismarckian and flat-rate
systems Beveridgean.
2
In 2001, public spending on old-age benefits was in average 6,4 percent of GDP in countries with flat-rate
benefits, and 9,4 percent in countries with earnings-related benefits (Disney, 2004; OECD, 2004).
1
and equity has (surprisingly for us) not been invoked in rationalizing why earnings-related systems are larger. The political economy literature has mainly focused on explaining the aggregate
size of social security (proxied by the contribution rate). Therein benefits are usually assumed
to be either perfectly flat-rate or earnings-related (see Galasso and Profeta (2002), Mulligan and
Sala-i-Martin (2004) for surveys and the seminal contributions by Browning (1975), Boadway
and Wildasin (1989), Cooley and Soares (1999), Tabellini (2000) and Boldrin and Rustichini
(2000)). An explanation for the stylized fact which relies on borrowing constraints has been
proposed by Casamatta et al. (2000). Our motivation for testing the role of labor supply distortions rather than the role of borrowing constraints in explaining the correlation derives from the
observation that in particular young, low-productivity individuals face borrowing constraints.
Analyses of voting behavior suggest that the politically decisive voter is advanced in age and
not necessarily of low-income (e.g. Cooley and Soares, 1999 and Sinn and Uebelmesser, 2002)
- a household type for which borrowing constraints play a diminished role. Thus, in our paper
capital markets are perfect and, to capture the role of age for voting behavior more thoroughly,
individuals work for two periods. The latter difference entails that even high-productivity individuals tend to support social security. When close to retirement, they view past contributions
as sunk and prefer a continuation of social security (Cooley and Soares, 1999 and Boldrin and
Rustichini, 2000).
Conde-Ruiz and Profeta (2004) analyze simultaneous voting on the type of social security
system and on its size. In their model, a smaller flat-rate system is supported by a voting
coalition of low-income individuals, who are in favor of a redistributive system, and highincome individuals, who are in favor of a redistributive system provided that the social security
contribution rate is smaller, so that they can invest their resources in the private capital market,
where they can earn higher returns. A large earnings-related system instead is supported by
the middle-income individuals. Different to our paper, Conde-Ruiz and Profeta (2004) take
labor supply to be exogenous. We show that labor supply distortions are sufficient to explain
the positive relationship between the degree of intragenerational redistribution and the size
of the social security system. As a consequence of our one-dimensional voting approach, our
explanation applies also to countries where the type of social security (earnings-related or flatrate) has been historically given. Also, we test our model by performing a numerical analysis,
calibrated on income distribution and social security rules in different European countries. To
the best of our knowledge, there exists no previous median voter analysis which empirically
relates cross-country differences in social security contribution rates to the redistributiveness of
social security.
Our paper is organized as follows. Section 2 presents our theoretical model. Section 3
presents the numerical analysis and Section 4 concludes.
2
2.1
The Model
Economy
Individuals differ in two dimensions: age and productivity. In each period there are three
overlapping generations: young, middle-aged and old. Each generation works for two periods,
1 and 2, and is retired in period 3. Individuals of each cohort differ in their productivity. We
index the productivity types so that the productivity is increasing in the index number, the
2
lowest productivity being denoted by one. While our theoretical framework holds with any
number J of productivity types, we restrict the number of productivity classes to five in each
age group in the numerical part of the paper. The induced productivity is allowed to vary over
the life-cycle. The productivity of a j-type individual, being young in period t is denoted as
ayj,t > 0. The productivity of a j-type individual who is middle-aged in period t is analogously
denoted as am
j,t > 0. All productivity parameters grow at the rate g. The number of workers
being of
Pa j type born in period t is nj,t , with the total size of the age-cohort born in period t
being j nj,t = nt . For simplicity, the proportion of each productivity type in the population
n
n
. The cohort size evolves according to nt+1 = (1+η)nt .
stays constant over time, i.e. nj,tt = nj,t+1
t+1
¢
¡
o
Preferences are given by a well-behaved utility function U = u cyj,t , cm
j,t+1 , cj,t+2 defined
over consumption when being young, middle-aged and old. Consumption of a j-type individual
born in period t is
¡
y
y ¢
− υ ayj,t , lj,t
(1)
− syj,t ,
cyj,t = (1 − τ t − τ w )ayj,t lj,t
¡
¢
y
m
m
m
m
m
cm
(2)
j,t+1 = (1 − τ t+1 − τ w )aj,t+1 lj,t+1 − υ aj,t+1 , lj,t+1 + (1 + r)sj,t − sj,t+1 and
o
m
(3)
cj,t+2 = pj,t+2 + (1 + r)sj,t+1 .
y
m
(lj,t
) denotes working hours by a j-type individual being young (middle-aged) in period
lj,t
y
m
t which gives a gross wage income ayj,t lj,t
(am
Without loss of generality the wage rate
j,t lj,t ).
y
each j-type individual receives per efficiency unit of labor supply, ayj,t lj,t
, is normalized to unity.
In the first period of life an individual of j-type derives utility from private consumption cyj,t
y
which is the net wage income, (1 − τ t − τ w )ayj,t lj,t
, minus the monetarized disutility of labor
¡ y y ¢
y 3
supply, υ aj,t , lj,t , and private savings sj,t . τ t and τ w are the social security contribution rate
and the general wage tax rate. The cost of labor supply υ(·) is continuous, strictly increasing
y
m
and convex in lj,t
and lj,t+1
, respectively. An analogous structure applies to consumption in the
second period of life. Old age consumption, coj,t+2 , is financed out of pension payments, pj,t+2 ,
and private savings, (1 + r)sm
j,t+1 , where r denotes the interest rate. There are no bequests.
Product and factor markets are perfectly competitive and market prices are exogenous for
the economy. The fixity of prices may follow from a linear production technology or in a small
open economy from factor price equalization in the presence of goods traded.4
2.2
Social Security System
We consider a pay-as-you-go (PAYG) social security system. Thus, total pension payments in
period t + 2, Pt+2 , equal contributions collected from the young and middle-aged in the same
period5 :
Ã
!
X
X
y
m
Pt+2 =τ t+2
(4)
nj,t+2 ayj,t+2 lj,t+2
+
nj,t+1 am
j,t+2 lj,t+2 .
j
j
3
Modelling the disutility from labor supply as a reduction in instantaneous consumption is common in
analyses of welfare programs, see e.g. Saez (2002) and Immervoll et al. (2004). An important implication of
this modelling choice is that all income effects are shifted onto consumption demand.
4
In this way, intergenerational linkages are exclusively formed by the unfunded social security system.
5
Notice that individuals pay a unique social security tax rate (not two, one for the earnings-related part and
one for the flat-rate part of the social security system).
3
The individual pension payment in period t+2 consists of a flat-rate and an earnings-related
component:
pj,t+2 = pt+2 + bj,t+2 .
(5)
In the earnings-related component, the benefit bj,t+2 is indexed to wage income in period
t + 1 and t according to the formula
¡
¢
y
m
m
bj,t+2 = θ xyt+2 ayj,t lj,t
+ xm
(6)
t+2 aj,t+1 lj,t+1 .
θxyt+2 and θxm
t+2 denote how income as young and middle-aged translate into pension claims
in period t + 2. The proportionality factors decompose into time-specific factors, xyt+2 and xm
t+2 ,
potentially allowing income earned as young and middle-aged to be treated differently in the
pension formula, and a time-independent factor, θ, frequently referred to as the Bismarckian
index. Straightforwardly, θxyt+2 and θxm
t+2 are zero in pure flat-rate system (θ = 0) and are
largest (ceteris paribus) in a pure earnings-related system (θ = 1). The pension formula (6)
fixes how the pension payment is related to the income history, but leaves it unspecified how
one euro collected in period t (and devoted to the earnings-related pillar) is spent on pension
claims gathered when being young and middle-aged. To fill the gap we assume that the link
between income in the first and second period of life and pension claims satisfies
xyt+i = xm
t+i (1 + r).
(7)
Residually determined, the flat-rate component pt+2 is
pt+2 = (1 − θ)
2.3
Pt+2
.
nt
(8)
Economic Equilibrium
We solve the model for the constant-elasticity specification
i
v(aij,t , lj,t
)=
γ i i 1+γ
a l γ ,
1 + γ j,t j,t
γ > 0,
i = y, m.
(9)
i
γ −1 is the elasticity of marginal disutility with respect to labor supply lj,t
. The disutility of
labor supply positively depends on the individuals’ productivity which captures the idea that
high income households face a higher opportunity cost of labor supply. Individual labor supply
and saving decisions in the first and second period follow from
¡
¢
o
max
U = u cyj,t , cm
s.t. (1) to (3), (5), and (6).
(10)
j,t+1 , cj,t+2
y
y
m
m
lj,t ,lj,t+1 ,sj,t ,sj,t+1
The individual first-order conditions can be written as
y
lj,t
:
m
:
lj,t+1
syj,t :
!
¡
y ¢
∂υ ayj,t , lj,t
∂u
(1 − τ t −
+ o θxyt+2 ayj,t = 0,
−
(11)
y
∂lj,t
∂cj,t+2
Ã
¡ m
¢!
m
,
l
∂υ
a
∂u
∂u
j,t+1
j,t+1
(1 − τ t+1 − τ w ) am
+ o θxm
am = 0, (12)
j,t+1 −
m
m
∂cj,t+1
∂lj,t+1
∂cj,t+2 t+2 j,t+1
∂u
∂cyj,t
−
Ã
τ w ) ayj,t
∂u
∂u
∂u
∂u
(1 + r) = 0 and sm
+ o
(1 + r) = 0.
y +
j,t+1 : −
m
m
∂cj,t ∂cj,t+1
∂cj,t+1 ∂cj,t+2
4
(13)
With the help of auxiliary variable χ, which is defined in the appendix and is independent
of the contribution rate, we can prove:
Lemma 1 Keeping τ t constant (τ t+i = τ t ), the economy has a balanced growth path in which
the individual labor supply in each working period is
µ
¶¸γ
∙
θχ
d
l(τ t ) = 1 − τ w − τ t 1 −
(14)
1+r
and the social security system offers as rates of return
xyt+i = τ t χ(1 + r) and xm
t+i = τ t χ.
χ measures the ratio of total wage income out of which pension benefits are financed in t + 2
over the aggregate life-cycle income of the contributors of the same age-cohort discounted to
the second period of life t + 1.
In what follows we consider the case of a dynamically-efficient economy. Thus, we find:
Lemma 2 In a dynamically efficient economy, χ is lower than 1 + r.
Labor supply is downward distorted by the general wage tax τ w . The negative impact of the
social security contribution rate τ t due to a reduction in wage income is counteracted by the link
between income and pension claims θχ. Implied by Lemma 2 the fraction of the contribution
θχ
rate which is considered a wage tax, 1 − 1+r
, is strictly positive for θ ∈ [0, 1]. Evident from
(14) labor supply is thus decreasing in the contribution rate where the distortion magnifies as
γ increases.
To clarify the implications of assumptions (7) and (9) for labor supply behavior, note that
the uniformity only applies to working time. Labor supply in efficiency units is heterogeneous for
different productivity types of the same cohort and over the life-cycle if individual productivity
changes over time. Individual preferences for social security are heterogeneous along both the
productivity and age dimension.
3
Political Equilibrium
As voters, citizens not only evaluate the impact of social security on their individual labor
supply, but also evaluate how the PAYG budget is affected by a change in the contribution
rate. Voting over the contribution rate takes place given the type of the social security system measured by θ.6 In order to focus on issues arising in voting on social security we take
τ w as given. Citizens decide upon the social security contribution rate by a once-and-for-all
voting. The identified political equilibrium can also be sustained in a repeated voting setting
by resorting to a suitable trigger strategy, see Koethenbuerger et al. (2005).
Formally, a j-type voter young in period t maximizes:
µ
¶
¡
¢
1
−
θ
y
y
m
m
m
d
[
u cc
(15)
Pt+2 + (1 + r)s[
j,t+1
j,t , cj,t+1 , τ t θ χ (1 + r)aj,t + aj,t+1 l(τ t ) +
nt
s.t.
(1) to (3), (4), (14) and (11) to (13).
6
Similar to Casamatta et al. (2000), the voting game is one-dimensional, since we assume that the type of
social security is more stable over time than the contribution rate, which may well adjust annually.
5
Variables with ab denote the optimal consumer choices derived from the household optimization problem analyzed in the previous section. Young voters compare the costs arising
from social security contributions, made as young and middle-aged, to the benefits they receive
as old.
Similarly, a j-type voter middle-aged in period t maximizes remaining life-time utility:
µ
¶
¡
¢d
1
−
θ
y
y
m
m
m
c
u c[
(16)
Pt+1 + (1 + r)sc
j,t
j,t−1 , cj,t , τ t θχ (1 + r)aj,t−1 + aj,t l(τ t ) +
nt−1
s.t.
(2) to (3), (4), (14) and (12) to (13).
For the middle-aged, contributions made when young are sunk. They just compare the cost
arising from social security contributions, made as middle-aged, to the benefits they receive as
old.
For any θ ∈ [0, 1], the benefit each pensioner receives is increasing in the social security budget. The elderly thus uniformly maximize utility by voting for the contribution rate arg max Pt .
The next proposition gives a characterization of how γ, τ w and the degree of intragenerational redistribution θ influence voting incentives.
Proposition 1 (i) For any given θ ∈ [0, 1], the preferred contribution rate of young, middleaged, and old voters is weakly decreasing in γ and τ w .
(ii) The young and middle-aged voters’ preferred contribution rate may be non-monotonic in
θ ∈ [0, 1] provided it is positive. The pensioners’ preferred contribution rate is weakly increasing
in θ ∈ [0, 1].
Increases in γ and τ w encourage voting for a lower social security contribution rate as both
increase the efficiency cost of social security financing. Earnings-related and flat-rate social
security components generate different voting incentives to the young and middle-aged voters
of different ability types. In a pure earnings-related social security system (θ = 1) young
voters prefer a zero contribution rate. The rationale is that an earnings-related pension system
χ
implicitly taxes contributions at a rate 1 − 1+r
> 0 in a dynamically efficient economy - see
Lemma 2. The young would prefer to eliminate the implicit tax burden by voting for a zero
contribution rate. If the continuation benefit outweighs the implicit taxation of the second
period’s contribution, the middle-aged will vote for a positive contribution rate. In a pure
flat-rate system (θ = 0), on the other hand, the coalition supporting social security generally
crosses different cohorts. High-income young and middle-aged individuals may jointly vote for
a lower contribution rate than e.g. low-income young and middle-aged individuals. In a mixed
system θ ∈ (0, 1) voting incentives tend to be a convex combination of voting incentives in the
polar cases.
A marginal increase of the earnings-related component of social security θ has two effects:
it reduces the efficiency cost of social security financing at the expense of less intragenerational
redistribution. For instance, provided that the politically decisive voter is middle-aged and
does not have a very low income, the net effect is that a higher θ results in a higher social
security contribution rate. Since the elderly uniformly vote for the contribution rate arg max Pt
a higher θ unambiguously increases their preferred contribution rate.
Preferences are single-peaked which renders the median voter politically decisive with majority voting on the contribution rate.
6
4
A Numerical Analysis
In this section we numerically compute the political-equilibrium social security contribution
rates for a sample of European countries. Restricted by data availability, the sample includes:
Austria, France, Germany, Greece, Italy, Portugal, Spain and the United Kingdom.7
Each country’s population is decomposed into three age groups and five income groups. For
each of these countries, we numerically solve for the social security contribution rate preferred
by each individual in each age and income group and subsequently identify the median voter.
Formally, we solve for the optimal choice of τ for each individual in each age and income group,
applying country-specific values for the exogenous variables (ε, r, θ, η, g, τ w ).
We simulate the equilibrium social security contribution rate using current data for population and productivity growth rate in each country (see table 1). Parameter values are inferred
from past performance during the last period of 20 years.
4.1
The Data
We consider three age-groups: young (aged between 21 and 40 years), middle-aged (aged between 41 and 60 years), old (aged between 61 and 80 years), and five income-groups of equal
size (very-low income, low-income ,intermediate-income, high-income, very-high income). Considering groups of equal size represents a “neutral” criterion to divide the population in the
same way in five income groups in all countries.
The data on the current population growth rate are taken from the European Community
Household Panel (ECHP), wave 1997.8 We calculate the number of individuals in each of the
three age groups, and obtain the dependency ratio, defined as the ratio between the number
of old individuals and the sum of young and middle-aged individuals. Calling ξ the growth
rate of population over one period, consisting of 20 years, the dependency ratio is equal to:
1/[(1 + ξ)(2 + ξ)], from which we can implicitly derive the value of ξ. Calling η the annual
population growth rate and given that (1 + η)20 = (1 + ξ), we derive the value of η shown in
table 1.
From the ECHP data set, we obtain data on productivity (wage earnings divided by the
number of hours worked) for each worker (young and middle-aged). For these two age groups,
we divide individuals in 5 income groups of equal size and calculate the average productivity
in each income group. We then calculate the overall average productivity for all young and
middle-aged. By dividing the average productivity in each income/age group by the overall
average productivity, we find the “productivity matrix” for each country, as shown in table 2.
Rows correspond to age groups (young, middle-aged) and columns to income groups (very-low
income, low-income, intermediate-income, high-income, very-high income).
We approximate g, the growth rate of average productivity, by the EUROSTAT data on the
average growth rate of per capita productivity in the period 1990-2003. The estimated value
of g is used to infer the earnings history of the currently middle-aged cohort from the earnings
of the current young cohort.
7
The data are taken from the European Commission Household Panel (ECHP). From the ECHP sample we
exclude Belgium, Denmark, Ireland, and the Netherlands because we do not have all necessary information and
Luxembourg, Finland, and Sweden because we have too few observations.
8
For a detailed description of the ECHP data see Nicoletti and Peracchi (2001).
7
Data on the tax rate on income without social security τ w (see table 1) are taken from
OECD Taxing Wages (2000) and refer to the average tax rate for a single person with no
children earning average income.
The value of θ is calculated as one minus the progressivity index of pension benefit formulae
obtained in OECD (2005) using microeconomic projections9 .
4.2
The Results
Our numerical simulations deliver a matrix of preferred contribution rates by age and income
group. We aggregate preferences through majority voting, by identifying the median voter and
his preferred tax rate. The results are summarized in table 3.
In our simulations, the median voter is always a high-income middle-aged individual, except
in Italy and Germany where he is a very-high income middle-aged. In line with the theoretical
analysis, we obtain a negative relation between the general wage tax τ w and the equilibrium
contribution rate τ (Proposition 1).
The most interesting result relates to the role of the earnings-related component of the
pension system θ. The simulation reveals a positive correlation between θ and the equilibrium
social security contribution rate τ taking the value of ∼ 0.87 (both when γ = 2 and γ = 1.5).
The rationale is that the median voter’s preferred contribution rate is most likely increasing in θ.
Reduced intra-generational redistribution makes social security more attractive to high-income
middle-aged individuals, at the same time as it reduces its efficiency cost.
In table 3 we also report the correlations between our simulated contribution rate and the
real (effective) contribution rate calculated by Disney (2004) - see table 1. The last line of
table 3 shows that our model performs quite well in explaining the real contribution rates.
The correlations between real (effective) values and our estimated values range from 0.9 (when
γ = 2) to 0.91 (when γ = 1.5).10
We have performed sensitivity analysis with respect to the Bismarckian index θ.11 Based
on ECHP data on wages and public pensions Conde Ruiz and Profeta (2004) compute the
Bismarckian index as the correlation between the level of post-retirement pension benefit (excluding occupational pensions)12 and pre-retirement earnings. Theoretically, in a pure flat-rate
9
The OECD index of progressivity is calculated as 100% minus the ratio of the Gini coefficient of pension
entitlements (considering only considers only mandatory parts of public pension programs) divided by the Gini
coefficient of earnings (expressed as percentages). Thus, one minus this index represents a synthetic measure of
the degree of redistributiveness of public pension programs.
10
Calibrating γ is inherently difficult. Note, given (14) γ is the elasticity of labor supply w.r.t. an increase
in the disounted net-of-tax income where income comprises wage income and pension payments, i.e. γ =
θχ
dt )
1−τ w −τ t (1− 1+r
)
∂ l(τ
> 0. In our model the labor supply elasticity w.r.t. instantaneous income
θχ
dt )
∂ (1−τ w −τ t (1− 1+r
l(τ
))
(which is typically estimated in econometric analysis of labor supply behavior) is thus well below γ. Also, since
in the simulation analysis γ relates to the labor supply elasticity over a time span of 20 years, in which intensive
and extensive labor supply decisions are made (Krueger and Meyer, 2002, and Immervoll et al., 2004), matching
γ with a empirical labor supply elasticity is notoriously diffícult. However, we should note that we tested other
values of γ for which the positive correlation between θ and the equilibrium social security contribution rate τ
prevailed at nearly the same level.
11
The detailed results are not reported in table 3. They are available upon request.
12
Occupational pension systems constitute the second pillar of old-age security whose financial importance
significantly varies across countries. All firm-based systems are run on a funded basis (Fenge et al., 2003) and
in our setting are equivalent to private savings. The Bismarckian index thus need not, and should not, include
8
system the correlation is zero and unity in an earnings-related system. The simulation shows
a correlation between θ and the equilibrium social security contribution rate τ of 0.88 and a
correlation between the simulated contribution rate and the real (effective) contribution rate
of 0.91 (when γ = 2 and r = 0.45).
5
Concluding Remarks
The relationship between the level to which benefits depend on past earnings and social security contribution rate has received little attention in the political economy literature, despite
its robustness. In this paper, we suggest an explanation based on a standard trade-off between economic efficiency and redistribution. The efficiency cost of redistributing income is
lower when benefits are earnings-related, encouraging voters who benefit from social security
to support higher contribution rates. Low income voters weigh this effect against the reduced
redistributiveness of more earnings-related systems. Our numerical analysis of several European countries suggests that the median voter model is able to explain the stylized fact that
intragenerationally more redistributive social security systems are smaller.
The social security contribution rates predicted by the median voter model also have a
strong correlation with the effective rates calculated by Disney (2004). This means that our
median voter model is able at least in part to explain the levels of contribution rates and their
cross-country differences. Even though our analysis focuses on steady-state political equilibria, our main result that benefit formula significantly affects political equilibrium contribution
rates can be expected to hold also outside of steady-states. This suggests that the political
response to population aging may crucially depend on to what extent benefits are linked to
past contributions. Accounting for the dynamic responses is left for future research.
6
Appendix
Proof of Lemma 1.
We first define three auxiliary variables
λy =
X
ayk,0 nk,0 , λm = (1 + g)
k
y
χ=
X
am
k,0 nk,0 ,
k
2
2
m
λ (1 + η) (1 + g) + λ (1 + η)(1 + g)
.
λm + (1 + r)λy
(A.1)
By the assumption of a balanced growth path, the rate of return offered by the PAYG system
m
stays constant over time. Then xyt+2+i = xyt+2 and xm
t+i = xt+i+1 ∀i ∈ {0, 1, 2, ...}. Denote these
steady-state values by xy and xm . By (7), xy = (1 + r)xm . (9) and the first-order conditions
(11) to (13) then imply
µ
∙
¶¸γ
θxy
\
.
l(τ t+i ) = 1 − τ w − τ t 1 −
1+r
occupational pensions.
9
As the labor supply is constant over time, so must be the share of PAYG benefits that go
to pay for benefit claims earned as young and middle-aged, respectively. Denote the share of
earnings-related PAYG benefits that goes to pay for the benefit claims accumulated as young
(middle-aged) by θy (θm ) > 0. As the total share of earnings-related benefits is θ, this implies
that
dt ).
(A.2)
θy θPt+2 = θxy λy (1 + η)t (1 + g)t l(τ
Analogously,
[
θm θPt+2 = θxm λm (1 + η)t (1 + g)t l(τ
t ).
(A.3)
Dividing (A.2) by (A.3) yields
θy
(1 + r)λy
=
.
θm
λm
As θy + θm = 1, we have
(1 + r)λy
λm
m
and θ = m
.
θ = m
λ + (1 + r)λy
λ + (1 + r)λy
y
Inserting this into (A.2) and (A.3) yields xy = τ t χ(1 + r) and xm = τ t χ. The proof is
completed by noting that these are identical to the values postulated in Lemma 1. Thus Lemma
1 indeed postulates a balanced growth path of the economy.
Proof of Lemma 2.
Inserting the expression for χ - see (A.1) - in the inequality χ − 1 < r and rearranging gives
(1 + η)2 (1 + g)2 λy + (1 + η)(1 + g)λm < (1 + r)2 λy + (1 + r)λm .
If the economy is dynamically efficient, (1 + η)(1 + g) < 1 + r, the inequality holds.
Proof of Proposition 1.
(i) Differentiating (14) w.r.t. τ t gives
θχ
dt )
1 − 1+r
dl(τ
= −£
¡
dτ t
1 − τw − τt 1 −
θχ
1+r
(A.4)
¢¤1−γ γ < 0.
In the proof we repeatedly make use of the auxiliary variable
ω t+i = λy (1 + η)t+i (1 + g)t+i + λm (1 + η)t+i−1 (1 + g)t+i−1 ,
i ∈ N.
For τ t+i = τ t ∀i ∈ N (once-and-for-all voting), the contribution rate preferred by a young,
j-type voter is solved as follows. First, differentiate (15) subject to (1) - (3), (4), and (14).
dt ), and inserting (A.4) yields
Using the envelope theorem, multiplying by 1/l(τ
Ã
µ
¶µ
¶
θχ
m
1 − 1+r
a
1
1−θ
j,t+1
y
¡
−aj,t −
1 − τt
1−
θχ +
1+r
1+r
nt (1 + r)2
1 − τw − τt 1 −
10
θχ
1+r
¢γ
!
ωt+2 .
(A.5)
By (A.5) and the non-negativity constraint, the preferred contribution rate of the young
voters belonging to the ability group j is given by
τ yj,t
´¡
³
⎧
⎫
¢ nt (1+r)2
am
j,t+1
1
⎨ (1 − τ )
⎬
1 − 1+r
θχ (1−θ)ω
+
1
−ayj,t − 1+r
t+2
w
³
´
¢
.
= max ¡
,
0
¢
¡
θχ
2
am
⎩ 1 − 1+r
−ay − j,t+1 1 − 1 θχ nt (1+r) + 1 + γ ⎭
j,t
1+r
1+r
(A.6)
(1−θ)ω t+2
Analogously, for τ t+i = τ t ∀i ∈ N (once-and-for-all voting), the contribution rate preferred
by a middle-aged, j-type voter is solved as follows. First, differentiate (16) subject to (1) - (3),
dt ), and inserting (A.4) yields
(4), and (14). Using the envelope theorem, multiplying by 1/l(τ
µ
m
−aj,t 1 −
¸Ã
¶ ∙
θχ
1 − 1+r
1
1
−
θ
1
y
¡
1 − τt
θχ + θχaj,t−1 +
ω t+1
1+r
1 + r nt−1
1 − τw − τt 1 −
θχ
1+r
¢γ
!
. (A.7)
Rearranging (A.7) and noting the non-negativity constraint, the preferred contribution rate
of middle-aged voters belonging to the ability group j is
τm
j,t
⎧
⎫
i−1
¢h
¡
y
⎪
⎪
1
1
1−θ
m
⎨ (1 − τ ) −aj,t 1 − 1+r θχ θχaj,t−1 + 1+r n ωt+1
⎬
+1
t−1
w
¢
.
= max ¡
,
0
i−1
θχ
¢h
¡
⎪
⎪
1 1−θ
⎩ 1 − 1+r −am 1 − 1 θχ θχay
⎭
+
ω
+1+γ
j,t
j,t−1
1+r
1+r nt−1
(A.8)
t+1
dt ), using (A.4) and reorganizing
The old maximize Pt subject to (14). Multiplying by 1/l(τ
gives
Ã
!
θχ
1 − 1+r
¡
¢γ ω t = 0.
1 − τt
(A.9)
θχ
1 − τ w − τ t 1 − 1+r
The preferred contribution rate of the old is given by
(
)
)
(1
−
τ
w
¢
,1 .
τ oj,t = min ¡
θχ
1 − 1+r
(1 + γ)
(A.10)
Given by (A.6), (A.8) and (A.10), the preferred contribution rate of any voter group is
weakly decreasing in τ w and γ.
(ii) By inspecting (A.6) and (A.8) the preferred contribution rates of the young and middleaged voters are non-monotonic in θ, while - following (A.10) - the preferred contribution rate
of the old is weakly increasing in θ.
References
[1] Blondal, S. and Scarpetta, S. (1998). The retirement decisions in OECD countries. OECD
W.P.
11
[2] Boadway, R.W. and D. E. Wildasin (1989), “A Median Voter Model of Social Security”,
International Economic Review, 30, 307-328.
[3] Boldrin, M. and A. Rustichini (2000), “Political Equilibria with Social Security”, Review
of Economic Dynamics, 3, 41-78.
[4] Browning, E. (1975), “Why the Social Insurance Budget is too Large in a Democratic
Society”, Economic Inquiry, 13, 373-88.
[5] Casamatta, G., H. Cremer, and P. Pestieau (2000), “The Political Economy of Social
Security”, Scandinavian Journal of Economics, 102, 503-522.
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[7] Cooley, T.F. and J. Soares (1999), “A Positive Theory of Social Security Based on Reputation”, Journal of Political Economy, 107, 135-160.
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[10] EUROSTAT, Statistics.http:/europa.eu.int/comm/eurostat/newcronos.
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Wirtschaftsforschung, No. 10, Munich.
[12] Galasso, V. and P. Profeta (2002), “The Political Economy of Social Security: A Survey”,
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Countries: A Microsimulation Analysis”, CEPR Discussion Paper No. 4324, London.
[14] Koethenbuerger, M., P. Poutvaara, and P. Profeta (2005), “Why are More Redistributive
Social Security Systems Smaller? A Median Voter Approach, CESifo WP # 1397, Munich.
[15] Krueger, A.B. and B.M. Meyer (2002), “Labor Supply Effects of Social Insurance”, Handbook of Public Economics, vol. 4, 2327-2392, North-Holland.
[16] Mulligan,
tures of
C. and X. Sala-i-Martin (2004), “Internationally Common FeaPublic Old-Age Pensions, and Their Implications for Models of
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the Public Sector”, Advances in Economic Analysis & Policy,
http://www.bepress.com/bejeap/advances/vol4/iss1/art4
4,
Article 4.
[17] Nicoletti, C. and F. Peracchi (2001), “Aging in Europe: What Can We Learn from the
Europanel?” in T. Boeri, A. Börsch-Supan, A. Brugiavini, R. Disney, A. Kapteyn and F.
Peracchi (eds), Pensions: More information, Less ideology. Kluwer, Dordrecht.
[18] OECD (2000), Taxing Wages, Paris.
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Economics, 102, 523-545.
13
Table 1: Data
Country
Austria
France
Germany
Greece
Italy
Portugal
Spain
UK
η
(%)
g (%)
1.30
1.39
1.76
0.52
1.62
0.78
0.91
2.04
2.10
2.00
1.60
3.00
1.80
2.50
3.00
1.80
θ
τw
0.793
0.536
0.771
0.957
0.960
0.689
0.870
0.304
0.098
0.134
0.215
0.022
0.193
0.067
0.121
0.158
effective contribution rate
τ eff
34.8
27.7
22.4
57.7
40.0
35.4
45.0
23.7
Source: η : authors’ calculations from the European Community Household Panel. g: taken from
EUROSTAT. θ taken from OECD (2005) as (1-progressivity index). τ w taken from OECD Taxing
Wages 2000 (average tax rate, excluding social security contributions, for a single person with no
children earning average income). τ eff taken from Disney (2004).
Table 2. Data on productivity levels
Very low
income
Low
income
Intermediate
income
Austria
High income
Very high
income
Young
0.422
0.703
0.859
1.0149
1.377
Middle-aged
0.613
0.88
1.0834
1.396
1.883
Young
0.354
0.622
France
0.768
0.999
1.451
Middle-aged
0.539
0.783
1.023
1.364
2.098
Young
Middle-aged
0.375
0.579
0.736
0.848
1.076
1.262
1.456
1.858
Young
Middle-aged
0.338
0.397
0.617
0.793
1.021
1.446
1.514
2.129
Young
Middle-aged
0.407
0.616
0.705
0.9207
1.031
1.353
1.341
1.774
Young
Middle-aged
0.346
0.411
0.564
0.677
0.907
1.284
1.797
2.727
Young
Middle-aged
0.249
0.485
0.554
0.839
0.945
1.571
1.573
2.371
Young
Middle-aged
0.257
0.213
0.715
0.765
1.164
1.272
1.725
2.037
Germany
0.895
1.019
Greece
0.777
1.13
Italy
0.862
1.133
Portugal
0.704
0.891
Spain
1.509
1.145
UK
0.905
1.003
Table 3: Results
r=0.05
Country
θ
Austria
France
Germany
Greece
Italy
Portugal
Spain
UK
0.793
0.536
0.771
0.957
0.96
0.689
0.87
0.304
corr( θ ,
corr( τ ,
τ
)
τ eff )
γ =2
γ =1.5
τ
τ
0.458
0.275
0.386
0.723
0.580
0.350
0.690
0.245
0.866
0.569
0.342
0.474
0.884
0.714
0.435
0.738
0.343
0.867
0.899
0.91
median voter
middle-aged, high-income
middle-aged, high-income
middle-aged, very high-income
middle-aged, high-income
middle-aged, very high-income
middle-aged, high-income
middle-aged, high-income
middle-aged, high-income